K. N. Volkov

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An approach for effective implementation of numerical methods and computational algorithms is developed to simulate flows of non-viscous and viscous compressible gas in the complex domains. The convergence speeding-up method of iterative process is discussed based on the usage of multi-grid technologies to the solution of large systems of finite difference equations. Euler and Navier-Stokes equations are quantized on structured and unstructured meshes with highresolution schemes in time and space. Multi-grid method is implemented on the basis of standard C/F splitting of variables and standard interpolation method. A specific approach is proposed to overcome the problems related to storing the matrix coefficients of different signs. A problem of flow around an airfoil is used to demonstrate the possibilities of computational tools developed. The results computed for non-viscous and viscous gas on structured and unstructured meshes are presented with the usage of various components of multi-grid technology. Comparison of computation speed and convergence factors on structured and unstructured meshes showed the economy of the developed approach and weak dependence of quality characteristics on the number of mesh points. The choice of optimal inner iterations number made it possible to decrease computation time for 10%. Obtained results can be applied while software creating for fluid dynamics problems in the complex configuration domains.

Keywords: computational fluid dynamics, unstructured mesh, multi-grid method, convergence, speeding-up

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